Simulation modeling презентация

the software when working over the last 260 hours

Simulation modeling

Using a random number, selected using tables or random number generators, it is necessary to simulate the occurrence of failures of the software within 10 hours

The number of failures in 1 hour

Frequency

the models describing processes close to reality. The results will be determined by the random nature of the process

Simulation is modeled by some random variable.
First, experimental data gives the frequency of occurrence of possible values of this variable.
Then based on frequencies the probability is calculated => the cumulative probability.
Knowing the cumulative probability, establish a correspondence between random numbers and the values of a random variable

the probability of the i event;
ωi – the frequency of realization of the i event;
N – the total number of events.

Cumulative risk is the sum of all peak probabilities, its value tends to 1. Depending on how many decimal places will have values of cumulative probability, we group the random numbers.

and got the following results on the dependence between the number of leakage channels and the damage

Using linear interpolation, find the value of any damages, if the company has 6 channels of leakage.

The number of leakage channels

Damage $

to the available discrete set of known values.

Linear interpolation is performed on the basis of formula P1(x) = ax + b of the function f, given in two points x0 and x1 of the interval [a, b]. The formula for linear interpolation is:

P1(x) - value of the function at the point x;
x - value of the point x;
x0 - value of the start point of the segment;
x1 -value of the end point of the segment;
f(x0) - value of the function at the starting point of the segment;
f(x1) - value of the function at the end point of the segment.

Guidelines for solution:

of the region for the last 6 months

For the 1st month a forecast of 13 leaks was given (by information security professionals). Using a simple exponential smoothing model, give the forecast on the number of leaks on the 7th month, if the smoothing constant α = 0.8

Month

Number of conf. inf. leakage

1 period ahead, which automatically corrects any forecast in the light of differences between the actual and the predicted result

The new forecast is determined by the formula

Ft+1 is the forecast value for a new period; α - the smoothing constant in the interval [0; 1]; At - the actual value at the last period; Ft - the forecasted value in the last period

Guidelines for solution:

years. If the value of α is close to one, it leads to the taking into account only the latest observations.



n – the number of observations included in the smoothing interval.


Uo (exponentially weighted average initial)
is solved in the following ways:
if there is data on the development of the phenomenon in the past, you can use the arithmetic average;
if there is no such information, the Uo is equated to the original first value in base forecast U1.

the reliability of forecasts in the 1 part of the 2014, provided that the information security specialists predicted the emergence of 25 new types of malicious programs, and as a result, the monitoring system discovered 33 new species of malicious program, 22 of them coincided with the experts forecasts.

the problem

Nпр = 25, Nнаст = 33, а Nнаст/пр = 22.

credibility /reliability and accuracy, as well as the errors of the 1st and 2nd kind.

credibility /reliability

Nнаст/пр – the number of occurred events, which was forecasted;

Nпр – the total number of events, which was forecasted.

Guidelines for solution:

predicted but did not occur, then this is an error of the 1st kind - α,

the 2nd kind - β